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The Difference Between Beta And Delta And Why We Care

Beta is one of the classic measurements within the financial industry. It is one of the first measurements shown on Yahoo Finance, right under the bid-ask and earnings estimate. Participants use it as a general gauge of market-related risk associated with an investment. As a reminder, an investment with a Beta of 0.8 is generally supposed to participate in 80% of a market move. So if the market increases 10% the investment should move up 8% and in a down 10% environment it should move down 8%. If only it was so simple… Beta is so well known that most people have not reviewed the basics of its calculation in a while, nor do they remember its drawbacks – let’s do some Beta 101! Beta is essentially the slope of the best fit line between the investment being studied (one axis of the graph) and the market (the other axis of the graph). The Beta for both examples above are 1, suggesting that each security very closely follows the market. However, in practice these two Betas are very different. The graph on the left demonstrates that the investment and the market have historically moved in tandem, as the best fit line approaches each plotted point very closely (i.e., very high correlation). Thus, the Beta of 1 is meaningful and appears to be predictive of the future. The graph on the right demonstrates a relatively random relationship between the investment and the market (i.e., low correlation); by some coincidence, the “best fit line” happens to lead to a perfect Beta of 1, which of course is meaningless – there is no reason to expect the investment and the market to move in tandem in the future. This illustration demonstrates one of the major drawbacks with Beta. If correlation is low, Beta is not useful and can even be misleading. Another drawback of Beta is related to the traditional compliance disclosure that past results are no guarantee of future results – Beta is a formulaic calculation based on historical measurements, and thus not necessarily a great predictor of what is to come. Take a look at Chipotle’s (NYSE: CMG ) 1 year rolling Beta below for a factual yet comical illustration of this – over a 5 year period, Beta ranged from 0 to 1.4. This drawback is exacerbated by yet another, which is the need to decide the correct historical time period – how far back is “meaningful”? Chipotle’s Beta on Yahoo Finance is .45, while Google lists Beta at .6 for Chipotle. Which one is right? These drawbacks collectively create a conundrum for investors looking to shape a portfolio by relying upon Beta. Let’s now discuss Delta. Delta is a lesser known term that is related to options. Like Beta, it is a measurement of the expected exposure to a referenced security. This is however where the similarities end. Beta, as mentioned, is a best fit line calculation between a given investment and a reference security; the reference security is typically the market (e.g., S&P 500 index), though it doesn’t have to be. Delta measures the expected exposure of an option to its reference security (e.g., the Delta of Apple (NASDAQ: AAPL ) options compared with Apple stock). It is calculated based on a few widely known variables, including the price of the reference security, the time to expiration of the option, and the implied volatility (future expected volatility as priced by the marketplace) of the option. Based on the way Delta is calculated, the value is current . Meaning that if the delta for an option is .8, then there is a very high likelihood that the option value will increase by approximately .8 for a $1 movement in the referenced security. For a call option, which provides the clients the right to purchase a stock, delta is bounded between 0 and 1 (i.e., if a security changes price, a call option following that security will change in the same direction somewhere between 0% and 100% – since a call option’s Delta can’t be negative, it won’t change in the opposite direction, and since Delta can’t exceed 1, it won’t change more than the security did). For a put option, which provides the clients the right to sell a stock, delta is bounded between 0 and -1. As a measurement, Delta cannot be used as broadly as Beta, since it can only be used with an option and the security the option follows. However, where it can be used, Delta is highly predictive of future relative exposure. Let’s look at Delta in practice. A visual illustration of Call Delta vs. price of the reference security follows – y axis is delta, x axis is how far the reference stock is trading from the strike price. For this option, when strike [1] = current market price (0% on the chart), Delta is about 0.5. As can be seen from the chart, Delta for an option changes as the reference security moves away from the strike price in either direction – Delta approaches 1 when the option is sufficiently in the money (e.g., stock is up about 30% vs. strike price), and Delta approaches 0 when the option is sufficiently out of the money (e.g., stock is down about 30% vs. strike). The implied volatility of the reference stock will affect how quickly Delta of an option changes as will the amount of time left to expiration – both conversations for another time. Let’s see how Delta works in action, starting with a simple example of a call option and then graduating to an options portfolio: Chart #1 is the classic shape of a call with time still left to maturity [2] . If the reference security declines below the strike, the loss is limited to the price paid for the option while if the reference security increases the call participates with the gains. Chart #2 shows the previous graph of Delta based on the relative value of the referenced stock vs. strike price. Using the data in Chart #2, one can predict relatively accurately how much the price of the call will increase and decrease based on an increase or decrease in the price of the reference security. Between the two charts, understanding ultimate exposure as well as relative exposure on a daily basis is very straightforward. For example, if the reference stock increased from 0% to 2%, the option should increase about 1% (Delta is about 0.5 for that range). However, if the reference stock increases from 30% to 32% (a 2% increase in total), the option value should increase about 2% (Delta is about 1 for that range). Now that we have the basics, let’s explore what happens when we combine options. Selling a “put spread” means we sell a put at a given strike and limit our downside by buying a put at a lower strike price – the lower the second strike price, the wider the spread, and the greater our risk (though the more premium we collect for taking that risk). Let’s discuss the maximum exposure of the spread. If we covered ourselves 12.5% below where we sold the first put, our maximum exposure can at most be 12.5%. If the market declines -25% by expiration, then the put we sold would be worth -25% and the put we bought would be worth +12.5%, for a net loss of 12.5%. On the other hand, if the market finishes flat or positive, our value is 0, since both the put we sold and the put we bought are worth 0. Can we figure out the Delta of the combined two option positions? Of course we can! A put spread is simply one long put and one short put so we can calculate the Delta of each and subtract. Below is a chart of the combined Deltas: Because we have two offsetting options, the Delta never goes to 1. Why? When the market is down significantly, the Delta for both puts is -1, so our long put and our short put result in a net Delta of -1 – (-1) = 0. This intuitively makes sense, because we know that once the market is down significantly more than -12.5%, it doesn’t matter if it’s down -30% or -40%, both puts are gaining value equally. If the market is up significantly, Delta for both puts is 0, bringing us back to a combined delta of 0. The above chart shows the combined Deltas with 4 months to go prior to the options expiring. As we mentioned earlier, both time to expiration and volatility have an effect on delta – following is an example of how time affects Delta. The following chart is an illustration of the same 12.5% put spread with 2 weeks left to maturity. As can be seen, a large Delta exposure is concentrated around the center of the spread with almost no delta once either put is surpassed. At any given point in time, the overall Delta can be calculated to give an accurate expectation of the price movement relative to the reference security. Now that we all have a deeper understanding of Beta and Delta, I would like to bring this all back to crafting investment strategies. A large component of the investing public looks to Beta as a guide in making investment decisions. However, for the reasons we’ve mentioned, Beta can be an ineffectual tool in portfolio planning. A product with a low historical Beta may exhibit a future decline far greater than the market for any number of reasons. As I’ve written about before, Funds and investment products often show a murky future, leaving a public averse to ambiguity unsatisfied with their investment options. So-called defensive strategies and tactical plays often seem to work for a period of time and abruptly stop working, leaving investors holding the bag (Contact me for many such examples). In the hands of an experienced user, option strategies are uniquely able to provide a strong level of transparency along with tangible levels of risk and reward. There are a growing number of strategies in the market that look to take advantage of options. For example, our Exceed Investments products are engineered to take advantage of the unique qualities of options in providing a more defined and controlled exposure to the market. In the same way that Delta provides a more mathematically true approximation of the future than Beta does, defined outcome investing can offer a level of predictability unattainable in traditional equity investing. [1] Strike is the value where the owner of a call has the contractual right to buy the stock and where the owner of the put would have the contractual right to sell the stock. For example, if Apple was trading $200 and the strike of the call was $195, the owner could exercise and buy at $195. If the strike of the call was $205, the owner would not exercise because they can simply buy it on the open market. (For reasons beyond the scope of this article, owners typically wait to expiration to exercise) [2] Options are term based, with a specific maturity date. In that sense, they are similar to bonds. As such, there is a level of premium attributable to the value prior to maturity. Again a topic for another time.

Active Vs. Passive Investing And The ‘Suckers At The Poker Table’ Fallacy

By Druce Vertes, CFA Image credit: ©iStockphoto.com/animatedfunk Warren Buffett sometimes says things that seem… contradictory. For example, in the “You don’t have to be a genius to be a great investor” category: ” Success in investing doesn’t correlate with IQ once you’re above the level of 25.” “If you are in the investment business and have an IQ of 150, sell 30 points to someone else.” He loves tweaking academic proponents of the efficient market hypothesis (EMH): “I’d be a bum on the street with a tin cup if the markets were always efficient.” ” Naturally the disservice done students and gullible investment professionals who have swallowed EMH has been an extraordinary service to us . . . In any sort of a contest – financial, mental, or physical – it’s an enormous advantage to have opponents who have been taught that it’s useless to even try.” And yet Buffett also says most people should steer clear of active investing: Like those same gullible investment professionals and misguided EMH proponents, he recommends low-cost index funds. “A low-cost index fund is the most sensible equity investment for the great majority of investors.” “My advice to [his own self-selected!] trustee could not be more simple: Put 10% of the cash in short-term government bonds and 90% in a very low-cost S&P 500 index fund. (I suggest Vanguard’s.) I believe the trust’s long-term results from this policy will be superior to those attained by most investors – whether pension funds, institutions or individuals – who employ high-fee managers.” How can Buffett say passive investing is best for most people and also an “enormous advantage” for active investors like him? If it helps everyone else, how can it also help him? The opposite view is sometimes described as the ” suckers at the poker table ” hypothesis – the theory that an increase in passive investing is bad for active investors like Buffett because the fewer suckers there are to fleece, the less profit there is for smart active investors. So which view is right? The “suckers at the poker table” theory, or Warren Buffett, who says passive investors make his job easier? And how can Buffett be right while at the same time saying most people should invest passively? Let’s do a simple thought experiment: What would happen if everyone was a passive investor except Warren Buffett? As is often the case, we find that Buffett is way ahead of everyone else. He is both correct and self-serving. Anyone can use an index to match the market on a holding period-return basis, and yet Buffett can still crush everyone else on a money-weighted basis. A brief theoretical digression: The Grossman-Stiglitz paradox holds that you can’t have a perfectly efficient market because that requires someone to be willing to arbitrage away any inefficient price. But arbitrageurs have to get paid. So they will only step in if they’re compensated for their time, data services, research, compliance, office rent, overhead, and an adequate after-tax, risk-adjusted return. So markets tend towards an equilibrium where prices are boundedly efficient, where there is no more mispricing than at the level that would make arbitrage profitable. The set of all investors is the market itself and, in the aggregate in any given period, earns the market return. The subset of index investors, by virtue of owning the market portfolio, also earns the market return. To make the indexers and non-indexers add up to the market, the non-index investors in the aggregate must also earn the market return. 1 In the aggregate, those “arbitrageur” active investors aren’t making any excess profits! Before expenses, they are matching the market, and after expenses they are underperforming. In order to have any profitable active investors, it seems you have to posit overconfident, “dumb” active money that loses money trading against the “smart” arbitrageurs. And that doesn’t make much sense. It implies the persistence of a class of irrational investors. If there’s a tug of war between smart money and dumb money, and a priori the dumb money is as strong as the smart money, and it’s to the smart money’s advantage to trick the dumb money whenever possible, why should that make prices efficient? It sounds like a theory of irrational traders and not very efficient markets. Let’s see if another thought experiment can shed some light: What happens if passive investors take over the market so there is only one active investor left: our hypothetical Warren Buffett? Let’s disregard for the moment changes in the composition of the index. We only have Buffett trading with passive investors. The passive investors just want to enter and exit the whole market. They don’t want to trade individual stocks or a non-market-weighted portfolio. And there are no other active investors to trade with other than Buffett, who makes a bid-ask market for the index, selling when it’s above his estimate of fair value and buying when it’s below fair value. A somewhat trivial example, which should be familiar to those who have done the CFA curriculum on holding period vs. money-weighted returns: Cash Flows Index Fair Value Index Price Premium/ Discount Holding Period Return Cost Averaging Investor 1 Dumb Investor 2 Dumb Investor 3 Warren Buffett Corporate Issuance Year 0 $ 100.00 100.00 0% (1,000) (1,000) (1,000) – 3,000 Year 1 $ 105.00 94.50 -10% -5.5% (1,000) – 945 (1,000) 1,055 Year 2 $ 110.25 121.28 10% 28.3% (1,000) (1,000) (1,000) 1,283 1,717 Final value $ 115.76 115.76 0% -4.5% 3,337 2,112 955 – Holding period return 5.0% 5.0% 5.0% 5.0% Money weighted return (IRR) 5.4% 2.7% -5.0% 28.3% The index fair value grows at 5% per year. It starts priced at fair value in Year 0, in Year 1, it trades at a 10% discount, in Year 2, at a 10% premium, and then finally returns to fair value in Year 3. The holding period return, which ignores flows, is 5%, matching the index. Dollar cost averaging Investor 1 buys $1,000 worth of stock each year and has a money-weighted return of 5.4% as a result of automatically buying more shares when they are cheap and fewer when they are expensive. Dumb Investor 2 panics when the market goes to a 10% discount and doesn’t buy that year and ends up with a 2.7% money-weighted return. Dumb Investor 3 panics even worse, sells when the market goes to a 10% discount, and ends up with a -5.0% money-weighted return. Warren Buffett stays out of the market until it trades at a 10% discount, sells at a 10% premium, and ends up with a 28.3% money-weighted return. Everyone gets the same 5% holding period return, which ignores flows. But on a money-weighted, risk-adjusted basis, of course, the returns are very different, and our Warren Buffett crushes the market. One way of looking at it is Buffett increases the size of the overall pie when the odds are in his favor, shrinks it when they aren’t, and outperforms without necessarily taking anything from the other investors, who earn the market return in each holding period. Another way of looking at it is to consider the whole scenario as one holding period during which Buffett took advantage of people who were selling low and buying high. Effectively, our Warren Buffett sets a floor under the market when events or cash flows make the passive investor inclined to sell excessively cheap and sets a ceiling when the market gets expensive. If you examine any individual year, everyone here is a passive investor in the sense of always holding the index. But if you think of the entire scenario as one holding period, only someone who owns the index and never trades is really a passive investor. Everyone else is buying high or selling low within the period. If you’re planning to invest for an objective other than buying and holding forever, you have to make decisions about when and how much to invest and when and how much to withdraw. On a sufficiently long timeline, the probability of being a completely passive investor goes to zero. Eventually, you have to make an active investment decision, and at that point, the shrewd investors are lying in wait. Everyone eventually has to pay Charon to cross the river Styx. It gets even better for Buffett when you incorporate index changes. An IPO comes out. The IPO is initially not in the index. Our hypothetical Warren Buffett sets the IPO price. He doesn’t have anyone to bid against or anyone to trade with besides the issuers since the stock is not yet in the index. Being an accommodating fellow, he sets the price at fair value minus his margin of safety, illiquidity discount, etc. The IPO eventually gets added to the index. Indexers have to buy the stock. Buffett solely determines the price at which it gets added to the index. In his obliging manner, he sets it at fair value for a liquid index stock plus a reasonable convenience premium. What a sweet deal! Pay a steep discount for any security not in the index and demand a big premium when they go into the index. Similar profits are available when securities exit the index. Going back to the Grossman-Stiglitz paradox, the arbitrageur active traders can do pretty well, even without the existence of a large pool of permanently underperforming “dumb money,” which is unnecessary and illogical. They pull a bit of Star Trek’s Kobayashi Maru scenario by going outside the bounds of picking stocks from within the index. The “suckers at the poker table” paradigm goes astray because there isn’t some exogenous fixed size of the investment pie investors are fighting over. The returns are endogenous: They are in part determined by how smart the investors are, how well the capital in the economy is allocated, and by everything else that impacts economic and market outcomes. The size of the profits pie is not fixed. When investors take a risk funding an early Apple (NASDAQ: AAPL ) or Wynn (NASDAQ: WYNN ), they increase the size of the overall pie, getting a bigger slice without taking a commensurate amount from everyone else. Smart money going into appropriately priced investment opportunities grows the whole pie. Dumb money going to bad businesses shrinks the pie. Once it’s not a strictly zero-sum game, you don’t need “suckers at the poker table” to outperform. Sufficiently smart money creates its own suckers. Bill Ackman, in his most recent Pershing Square letter, asked “Is There an Index Fund Bubble?” He pointed out that if index funds generally side with management, they make the activist’s job harder. But increased herding can be a self-fulfilling prophecy with bubble dynamics, and it increases opportunities outside liquid indexes. There are useful parallels between investing and poker , but investing is not a zero-sum game, dumb money is not the primary driver of returns for most strategies, and the “suckers at the poker table” is not a useful analogy for most long-term investors. 1 This accounting excludes issuers of stock, who are kind of important. Companies are net distributors of cash to their stockholders. They pay dividends and they on net buy back stock , these days. So everyone cannot be a passive investor in the S&P and reinvest dividends. If they tried, something would have to give. Investors would bid up stocks until someone capitulated and started selling, or companies started issuing stock, or something. When it’s not a zero-sum game, reasoning from accounting identities tends to be misleading. Disclaimer: Please note that the content of this site should not be construed as investment advice, nor do the opinions expressed necessarily reflect the views of CFA Institute.

Should REIT Investors Only Use A Buy And Hold Strategy?

Using REITs as an example I respect Brad’s expertise and experience in identifying the better choices of long-term, income-growth REITs. I have no such credentials. So I took his choices as listed in his report, and only included those where my special information could contribute. What I bring to the party is the daily updated next few months’ price range forecasts of market-makers [MMs] for over 2,500 widely-held and actively-traded equities, including hundreds of REITs. Their forecasts are derived from their hedging actions (real money bets) taken to protect firm capital required to balance buyers with sellers in filling volume block trade orders of billion-$ fund management clients who are adjusting portfolio holdings. Those forecasts are forward-looking additions to the reward/risk challenge, providing explicit downside price exposure prospects, as well as comparable upside gain potentials. Conventional risk/reward evaluations usually are based on only one forward-looking dimension: EPS and its growth potential. Everything else is drawn from history. Past P/E ratios and past price behaviors. Worse yet, the downside guess is typically a symmetrical measure (standard deviation) of price change, including upside differences from a mean value as well as downside ones. And the longer-term historical periods measured assume that neither the size of the variances nor their upside to downside balance varies over the time period. The assumption is that “risk” is static. Do today’s market prospects look like they did six months ago? Or a year ago? We also use history as a guide. But we try to make more sensible comparisons, because we have the information at hand to do so. We can look to the history we have collected live as the market has evolved daily in the past 15+ years since Y2K. We know what was being estimated by those arguably best-informed pros in the market, in terms of their stock-by-stock, day-by-day real money self-protecting actions. Real behavioral analysis of folks doing the most probable “right” things, not everyday man making errors of perception. We look to see how prices actually changed following prior forecasts that had upside-to-downside balances like those being seen today. And recognizing that today’s competitive scene continues to evolve, we limit our look back to the most recent five years, 1,261 market days. How that looks for this sample of REITs Click to enlarge This table has columns of holding periods following the date each forecast was made, increasing cumulatively up to 16 weeks of five market days. It has rows showing the annual rates of change (CAGRs) in each of the holding periods, for the forecasts counted in the #BUYS column. Those forecasts are a total in the blue 1: 1 row, so they are the average of the several REITs. The row above the blue row includes about half of the total sample, counting all forecasts where the upside prospect was twice the downside, or better. The next higher row includes only those forecasts where the upside was three times the downside. That process continues to the top row where only the forecasts that had huge positive upside balances, or had no downside at all, existed. The bottom half of the table below the blue row is just the inverse of the top half. In some ways, it is the more interesting part of the table. It shows that for these REITs the MMs pretty well identified the points in time where price problems were upcoming. It also shows that those issues would eventually recover, and at a later date probably be part of the forecasts shown in the upper half of the table. It also justifies the notion that if time is not a problem for the investor (he/she has adequate financial resources to deal with current retirement needs or sufficient time remaining before retirement to get there), then buy and hold works for them as a strategy in these cases. But if time is closing (or has closed) in on the retiree, then an active investment strategy of moving away from troubled REITs and into more favorably positioned ones can provide capital gains, along with the payout income of the alternative. It takes work and attention that is not required with B&H. But the CAGRs that can be added are not trivial. The REIT illustration has broader application Brad makes a strong case that, focused as he is on REITs, they should make up only a minor part of the investor’s portfolio. The table he uses from asset manager 7Twelve, showing year-by-year returns for various asset groups is instructive. Here is a copy of that table: Click to enlarge It has to be enlarged to be readable, but it is worth the effort. The yellow-highlighted years of best asset performance HOLLER * for attention to active asset-class portfolio management if you expect to beat the “market” average. The simple arithmetic average of the best asset gains each year was +31% and the worst averaged -14%. What typically is taken as the “market” average year was +5% simple, but the CAGR for the S&P 500 over the 15 years is about zero. *(A little Maine human: I had an Uncle who sometimes referred to advertising “written in letters large enough that you had to holler to read ’em”). Robyn Conti’s survey of investors in retirement showed that only 55% of them had over $200,000 portfolios. Of that 55, 31% had over $1 million. Some 5% admitted to less than $200,000 and the other 40% may have none. Trying to live better than social security and what a 401(k) plan may provide is pretty tough from even an 11% yield on $200,000 if it all was in REITs at the above table’s average. But as Brad makes clear to all nest featherers, we should use several baskets. Trouble is, the varied asset classes all present active-management alternatives if you have the insights. Here is how the Dow Jones stocks have fared over the past five years, based on MM forecasts: Click to enlarge Clearly, over the last five years, there have been hundreds of instances in these 30 stocks where substantial lasting capital gain advantages could be had, and as many or more where major capital calamities could be avoided. And these are the most closely watched stocks. Bigger and more frequent increments are being offered regularly elsewhere. Conclusion For many retirees, (the 31% in Robyn Conti’s survey with over $1 million portfolios and some of the 24% slightly less well-heeled), where REIT investments are concerned, buy and hold is a well-earned and satisfying strategy. But both her report and Brad Thomas’ advice open the consideration of earning more comforting resource reserves by the investor taking an active part in building and maintaining a more rapidly growing portfolio. We are particularly sensitive to the problems of those within 15 years of retirement who, by buy and holding SPY or similar market-average investment, may have lost any opportunity for growth over the last 15 years. They probably can’t afford to repeat that experience without a love for a future greeter role at the local Wal-Mart.